In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, - 2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the

Question

In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, - 2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets 5 marks is _____

Quantrex Academy · Accepted Answer

Correct answer: 0

Let the marks obtained in each of the five MCQ be x 1 , &#160; x 2 , &#160; x 3 , &#160; x 4 , &#160; x 5 Now, x 1 + x 2 + x 3 + x 4 + x 5 = 5 Only one possibility satisfies the above equation i.e. 3 , 3 , 3 , - 2 , - 2 Hence, total number of ways = 5 ! 3 ! 2 ! &#215; 2 &#215; 2 = 40

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